Please show e every step please

Question

1. Earth = 9.8 meters per second squared [m/s^2]
2. Earth's moon = 1.6 meters per second squared [m/s^2]
3. Mars = 3.7 meters per second squared [m/s^2]

The Eco-Marathon is an annual competition sponsored by Shell Oil, in which participants build special vehicles to achieve the highest possible fuel efficiency. The Eco-Marathon is held around the world with events in the United Kingdom, Finland, France, Holland, Japan, and the United States.

A world record was set in Eco-Marathon by a French team in 2003 called Microjoule with a performance of 10,705 miles per gallon [mi/gal]. The Microjoule runs on ethanol.

Assume the Microjoule is taken to Mars and given 100 grams [g] of ethanol (specific gravity = 0.789).

If the car is driven until the fuel runs out, how far did the Microjoule drive on Mars in units of kilometers [km]?

Answer 1

I think this can be answered only under several assumptions, such as

identical conditions on Mars and Earth (besides gravity).

- completely flat road on both planets,

- identical coefficient of friction on both planets,

- no atmospheric resistance on both planets,

- US gallons, not imperial gallons.

If my assumptions are wrong then please ignore this.

Let

E_e = 10,705 mi/gal = 4551 km/liter be the mileage on Earth,

E_m (unknown) be mileage on Mars,

m = 100 g be the mass of given ethanol,

r = 0.789 g/cm³ be ethanol's specific gravity,

V = m/r = 100/0.789 = 127 cm³ = 0.127 liter be the volume of given ethanol,

g_e = 9.8 m/s² be Earth's gravitational acceleration

g_m = 3.7 m/s² be Mars's gravitational acceleration

The energy of the fuel gets converted completely into heat due to road friction.

The force of friction is the coefficient of friction times weight.

Since weight on mars is reduced by the factor of g_m/g_e, friction is reduced by the same factor.

Therefore mileage is increased by the same factor.

The distance travelled is

s = V × E_m = V × E_e × g_e/g_m = 0.127 × 4551 × 9.8/3.7 = 1531 km